A widely known power supply device includes a secondary battery such as lithium-ion battery, and backs up supplying of power from the secondary battery if a commercial alternating current power supply fails to supply electric power. Such a power supply device can sometimes be used for so-called peak shaving or peak shifting electric power to be used to lower a maximum value of use of commercial electric power in daytime by setting the power supply device to charge electricity in a night time zone, and discharge electricity in a daytime zone during which electric power is used in a large amount. Firmware is generally used to achieve a function for charging and discharging of the secondary battery and a function for protecting the secondary battery if an abnormality occurs. Such firmware is normally incorporated in the power supply device. However, when the firmware incorporated in the power supply device is updated for adding functionality, and for correcting failures, the functions achieved through the firmware might be stopped during updating, thus, some operations set by a user could not be achieved. With a conventional method, firmware is temporarily updated, any error in a battery pack is detected, a check is performed again if an error is detected, and the firmware is actually updated when no error is detected in a re-check for errors (see PTL 1 shown below).